Equal-intensity waves in non-Hermitian media

Area of Science:

• Photonics
• Wave Physics
• Non-Hermitian Systems

Background:

• Non-Hermitian photonics explores systems with gain or loss, offering unique wave phenomena.
• Localized paraxial solutions in complex guided structures are of significant interest.
• Understanding wave behavior in homogeneous media provides a baseline for complex systems.

Purpose of the Study:

• To introduce and characterize a novel class of waves, termed equal-intensity (EI) waves, in non-Hermitian photonic systems.
• To establish a connection between free-space wave solutions and EI waves in non-Hermitian media.
• To explore the potential applications of EI waves in diverse physical problems.

Main Methods:

• Analysis of complex guided structures supporting localized paraxial solutions.
• Mathematical formulation relating non-Hermitian potentials to phase and amplitude of bulk solutions.
• Investigating the properties of EI waves through their connection to free-space plane waves and Gaussian beams.

Main Results:

• Identification of a class of complex guided structures supporting EI waves.
• Demonstration that EI waves possess identical intensity distributions to corresponding free-space solutions, differing only in phase.
• The non-Hermitian potential is directly linked to the phase of the free-space solution and the potential's real and imaginary parts.

Conclusions:

• EI waves provide a new paradigm for studying wave phenomena in non-Hermitian photonics.
• The established relationship facilitates the investigation of EI wave propagation in random media, interface lattice solitons, and moving solitons.
• Further research can explore EI waves' connection to unidirectional invisibility and Bohmian photonics.